Computer simulation of grain growth—I. Kinetics
Abstract
A novel Monte Carlo procedure is applied to the study of the kinetics of grain growth in two dimensions. The model employed maps the microstructure onto a discrete lattice. Each lattice site is assigned a number, between 1 and Q, which indicates the local crystallographic orientation. The initial distribution of orientations is chosen at random and the system evolves so as to reduce the number of nearest neighbor pairs of unlike crystallographic orientation. The temporal evolution of the microstructure is monitored to yield the time dependence of the size and shapes of the grains. The microstructures produced are in good correspondence with experimental observations of soap bubbles, foams and cross-sections of isotropic metallurgical specimens. Examination of the temperature and lattice dependence of the kinetics shows the existence of a number of universal features. The model properly reproduces the kinetics of the Ising model in the limit that Q approaches 2. For large Q, power law kinetics [Rm(t) − Rm(0) = Bt] are observed with the growth exponent, m, is found to be independent of Q with a value of approximately 2.4. The deviation of the growth exponent from the mean field value of 2 is discussed in terms of the role of vertices.
Résumé
Nous appliquons un nouveau procédé de Monte Carlo à l'étude de la cinétique de la croissance de grains à deux dimensions. Le modèle que nous utilisons applique le microstructure sur un réseau discret. Chaque site du réseau est numéroté de 1 à Q, ce qui indique l'orientation cristallographique locale. Nous choisissons une répartition initiale des orientations aléatoire et le système évolue de manière à réduire le nombre de paires de premiers voisins d'orientations cristallographiques différentes. Nous enregistrons l'évolution temporelle de la microstructure afin d'obtenir la variation de la taille et des formes des grains en fonction due temps. Les microstructures produites sont en bon accord avec les observations expérimentales de bulles de savon, d'écumes et de sections d'échantillons métallurgiques isotropes. L'examen de la variation de la cinétique en fonction de la température et du réseau montre qu'il existe un certain nombre de caractères universels. Notre modèle tend vers la cinétique du modèle d'Ising lorsque Q tend vers 2. Pour les fortes valeurs de Q, on observe une cinétique en loi de puissance [Rm(t) − Rm(0) = Bt], l'exposant de la croissance m étant indépendant de Q et valant approximativement 2.4. Nous discutons l'écart de la valeur de l'exposant de la croissance par rappon à la valeur 2 de champ moyen en fonction du rôle des sommets.
Zusammenfassung
Die Kinetik des Kornwachstums in zwei Dimensionen wird mit einer neuartigen Monte-Carlo-Prozedur untersucht. Das zugrundeliegende Modell bildet die Mikrostruktur auf ein diskretes Gitter ab. Jeder Gitterplatz erhält eine Nummer zwischen l und Q, welche die lokale kristallographische Orientierung angibt. Die Orientierungsverteilung zu Anfang ist zufällig. Das System entwickelt sich dergestalt, daβ die Anzahl von Paaren aus nächsten Nachbarn mit ungleicher kristallographischer Orientierung verringert wird. Die zeitliche Entwicklung der Mikrostruktur wird aufgezeichnet und im Hinblick auf die Zeitabhängigkeit von Korngröβen und -form ausgewertet. Die sich einstellenden MikroStrukturen entsprechen den an Seifenblasen, an Schaum und an Querschnitten von isotropen metallurgischen Proben gemachten Beobachtungen gut. Die Analyse der Temperatur- und Gitterabhängigkeit der Kinetik weist auf eine Anzahl universeller Eigenschaften hin. Das Modell gibt die Kinetik des Isingmodelles in der Grenze Q gegen 2 getreu wieder. Bei groβen Q werden Potenzgesetze in der Kinetik beobachtet [Rm(t) − Rm(0) = Bt]. Der Wachstumsexponent m ergibt sich als unabhängig von Q und hat einen Wert von ungefähr 2.4. Seine Abweichung vom mittleren Feldwert von 2 wird anhand der Rolle von Scheitelpunkten diskutiert.
References (42)
- M Hillert
Acta metall.
(1965) - N.P Louat
Acta metall.
(1974) - P Feltham
Acta metall.
(1957) - V.Yu Novikov
Acta metall.
(1978) - V.Yu Novikov
Acta metall.
(1979) - O Hunderi et al.
Acta metall.
(1979) - O Hunderi et al.
Acta metall.
(1981) - G.F Bolling et al.
Acta metall.
(1958) - J.P Drolet et al.
Acta metall.
(1968) - D.J Srolovitz et al.
Acta metall.
(1984)
Scripta metall.
J. comput. Phys.
Acta metall.
Acta metall.
Acta metall.
Recrystallization of Metallic Materials
Recrystallization of Metallic Materials
Metall. Trans.
Trans. Am. Inst. Min. Engrs
J. Am. Ceram. Soc.
J. Am. Ceram. Soc.
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